Statistical Methods in Finance 2025

Computational Implementation of Heston, CIR2, HJM and LIBOR Market Models

By:Parth Mohan Misra
Indian Institute of Management, Ahmedabad

This study implements major continuous‐time models used in modern derivatives and interest‐rate markets. Beginning with the Heston model (1993) for stochastic volatility, Monte Carlo simulations replicate option prices which closely match analytical benchmarks, thereby validating the computational framework. The analysis is then extended to the two‐factor Cox–Ingersoll–Ross model of Chen & Scott (1992), where numerical solutions of the underlying differential equations accurately reproduce published bond prices. The Heath–Jarrow–Morton framework (HJM) is applied to both simulated and empirical forward rate data from the Federal Reserve Bank of St. Louis FRED database, revealing that one or two volatility factors explain over 99 % of yield‐curve variation. Finally, the LIBOR Market Model (LMM) is calibrated to market-implied volatilities per Brigo & Mercurio (2006). The results demonstrate that advanced continuous‐time models can be efficiently implemented in R.